利用有限域上二元多项式构造带仲裁的认证码

摘要

It is assumed that the transmitter and the receiver trust each other and they do not cheat in a traditional unconditionally secure authentication code. But it is not always like this,a transmitter may deny sending a message which he actually sent and a receiver may try to construct a fraulent message on behalf of the transmitter,in this case,an arbiter is needed in the situations just mentioned. Authentication codes with arbitration can solve the problem that the transmitter and the receiver distrust with each other in the correspondence system. An authentication code with arbitration from binary polynomials over finite fields is given and their parameters are computed. Assuming that the encoding rules chosen according to a uniform probability distribution,the probabilities of a successful impersonation and a successful substitution by the opponent,a successful impersonation by the transmitter,a successful impersonation and a successful substitution by the receiver are also computed.%在传统的无条件安全认证码中,假定发方和收方是相互信任的,他们不会互相欺骗.但有些情况也可能不是这样,发方在发出一个消息后,不承认是他发的,收方捏造了一个消息,声称来自发方,在这种情况下就需要增添仲裁方.带仲裁的认证码能解决通信系统中发方与收方互不信任的问题.利用有限域上二元多项式构造了一个带仲裁的认证码,并计算了所构造码的参数.当编码规则按等概率分布选取时,计算出了敌方与收方成功模仿攻击和成功替换攻击的最大概率,以及发方成功模仿攻击的最大概率.